Dispersion dipoles and dispersion forces: Proof of Feynman’s ‘‘conjecture’’ and generalization to interacting molecules of arbitrary symmetry

This paper provides the first explicit, general proof that the leading-order dispersion forces between two interacting molecules result from the attraction of nuclei in each molecule to the dispersion-induced change in the electronic charge density of the same molecule. The proof given here holds for molecules of any symmetry, provided that overlap between the charge distributions is small. New sum rules for the nonlinear response tensors are also obtained, after consideration of the long-range limit. A perturbation analysis gives the dispersion-induced polarization in each molecule in terms of nonlocal, nonlinear response tensors taken at imaginary frequencies. Forces on the nuclei are computed from a reaction-field expression for the dispersion energy, in terms of polarizability densities. Recent work has shown that the derivative of the polarizability density with respect to a nuclear coordinate is linked to an integral involving the nonlinear response tensor and the dipole propagator, and this link provides the key to the proof.